Re: Erf funcion

*To*: mathgroup at smc.vnet.net*Subject*: [mg123948] Re: Erf funcion*From*: Szabolcs Horvát <szhorvat at gmail.com>*Date*: Mon, 2 Jan 2012 02:43:30 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jdp256$rqi$1@smc.vnet.net>

I'd like to link to the same question asked earlier here: http://stackoverflow.com/questions/8523505/using-alternative-special-functions-in-simplify-and-expand There is one (partial?) answer there. Vicent mentioned there that he would like to get expressions in terms of FiX, while keeping the definition FiX[x_] := ... I believe this is not possible (except perhaps through some formatting tricks with Defer/HoldForm) On 2012.01.01. 8:31, Vicent wrote: > Hello. > > I have an expression that depends on the Cumulative Distribution > Function (CDF) of a Normal Variable with mean = 0 and standard > deviation = 1. > > When I perform operations and/or derivatives with/for that function > with Mathematica, I get expressions involving Erf function, as the CDF > function of a Normal distributed variable and Erf (error function) are > closely related. Concretely, > > FiX[x] == (1/2)*(1 + Erf[x/Sqrt[2]]) > > and thus > > Erf[x] == 2*FiX[x*Sqrt[2]] - 1 > > where FiX stands for the previously mentioned CDF, I mean: > > X = NormalDistribution[0, 1] > FiX[x_] := CDF[X, x] > > > Is there a quick way to ask Mathematica not to use Erf but always > let the results as a function of FI[x]?? > > The expressions I get as a result of my computations are larger than > this short example: > > 3 (2^(7/2 - 2 (k + t))) Cp ( E^(-d^2 - (36 Cp^2)/lambda^2)) > ((Erf[(-d + (6 Cp)/lambda)/Sqrt[2]] + Erf[(6 Cp + d lambda)/(Sqrt[2] > lambda)])^k) > > where "Cp", "k", "t", "d" and "lambda" are parameters or arguments > that I want to keep as "generic". > > So, how can I "translate" expressions such as the last one into "FiX > mode"? Or, better, how can I prevent Mathematica to reduce everything > to "Erf mode"?? > > I hope my question is clear enough... :) > > Thank you very much in advance for your answers. > > And have a good new year! > > -- Szabolcs Horvát Mma QA site proposal: http://area51.stackexchange.com/proposals/37304